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Maths problems from University entrance exam past papers and the BMO

Primitive Roots of Unity
8:28
Primitive Roots of Unity
Always Irrational, Sometimes Irrational: STEP II + Extension
7:58
Always Irrational, Sometimes Irrational: STEP II + Extension
3D Centroid: STEP Vectors
5:19
3D Centroid: STEP Vectors
The tan(θ/2) Substitution
6:15
The tan(θ/2) Substitution
How did the Chicken Cross the Road? Cambridge Entrance Exam
5:16
How did the Chicken Cross the Road? Cambridge Entrance Exam
Perpetually Perpendicular Polar Differential Equations
7:06
Perpetually Perpendicular Polar Differential Equations
Unimodal Series
10:14
Unimodal Series
Sum Factorial Fun
5:39
Sum Factorial Fun
Hyperbolic Trig: STEP III 2016
7:52
Hyperbolic Trig: STEP III 2016
Complex Number Loci: STEP 2011
6:47
Complex Number Loci: STEP 2011
Exponential Matrices
6:46
Exponential Matrices
Matrices: STEP III
7:31
Matrices: STEP III
Periodicity: STEP II
5:28
Periodicity: STEP II
Geometry, Algebra, or Vectors? STEP II 2014
4:24
Geometry, Algebra, or Vectors? STEP II 2014
Parametric Parabolae
4:15
Parametric Parabolae
Vector Cones: 2010 STEP II
5:30
Vector Cones: 2010 STEP II
Symmetry: STEP II 2009
5:05
Symmetry: STEP II 2009
Quadratic Trigonometry
5:15
Quadratic Trigonometry
Logarithms and DoTS: STEP 2012
5:12
Logarithms and DoTS: STEP 2012
Painkillers: Differential Equations
6:52
Painkillers: Differential Equations
Mathematical Wordsworth: Rhyme Schemes
5:51
Mathematical Wordsworth: Rhyme Schemes
Proof by Contradiction: Cambridge Entrance Exam
4:35
Proof by Contradiction: Cambridge Entrance Exam
Tending Towards e: STEP III 2000
4:10
Tending Towards e: STEP III 2000
Primitive Roots of Unity
5:38
Primitive Roots of Unity
Scary Vectors Question
8:06
Scary Vectors Question
Incorrect Algebra: 2003 STEP I
4:08
Incorrect Algebra: 2003 STEP I
Floor Reciprocals: STEP I 2013
9:04
Floor Reciprocals: STEP I 2013
Simplex Algorithm: Easy Linear Programming
5:50
Simplex Algorithm: Easy Linear Programming
Logarithms and Maclaurin: STEP III
6:23
Logarithms and Maclaurin: STEP III
More Vectors: STEP II 2011
4:24
More Vectors: STEP II 2011
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